Question

A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible. a. What is the largest number of groups that could be formed? groups b. If that many groups are formed, how many students of each grade level would be in each group? sixth-grade students and seventh-grade students

Answer 1

1. 15 groups. The greatest common factor of 75 and 90 is 15. 2. 6 sixth-grade students and 5 seventh-grade students

2. 6 sixth-grade students and 5 seventh-grade students ( 6 ⋅ 15 = 90 and

5 ⋅ 15 = 75 )

Answer 2

a) 15 is the largest number of groups that can be made.

b) There would 6 sixth grade students and 5 seventh grade students in each group.

Explanation:

Number of sixth-grade students = 90

Number of seventh-grade students = 75

a) What is the largest number of groups that could be formed?

Since the music director wants to make groups with the same combination of sixth and seventh grade students in each group,

The greatest common factor (GCF) of the number of sixth and seventh grade students would give us the required combination.

Factor of 90 = 2*45 = 2*3*15 = 2*3*3*5

Factor of 75 = 3*25 = 3*5*5

The greatest common factors are 3 and 5

GCF = 3*5 = 15

Therefore, 15 is the largest number of groups that can be made.

b. If that many groups are formed, how many students of each grade level would be in each group?

Sixth grade = 90/15 = 6

Seventh grade = 75/15 = 5

Therefore, there would 6 sixth grade students and 5 seventh grade students in each group.